This article concerns mesh restrictions that are needed to satisfy several important
mathematical properties—maximum principles, comparison principles, and the nonnegative …

The flow of incompressible fluids through porous media plays a crucial role in many
technological applications such as enhanced oil recovery and geological carbon-dioxide …

Predictive simulations are crucial for the success of many subsurface applications, and it is
highly desirable to obtain accurate non-negative solutions for transport equations in these …

We present a robust computational framework for advective–diffusive–reactive systems that
satisfies maximum principles, the non-negative constraint, and element-wise species …

SUMMARY A new monotone finite volume method with second‐order accuracy is presented
for the steady‐state advection–diffusion equation. The method uses a nonlinear …

We present a novel computational framework for diffusive–reactive systems that satisfies the
non-negative constraint and maximum principles on general computational grids. The …

The aim of this work is to propose a monotonicity-preserving method for discontinuous
Galerkin (dG) approximations of convection–diffusion problems. To do so, a novel definition …

In this paper, two repair techniques are proposed for diamond schemes of anisotropic
diffusion problems to ensure that the repaired solutions satisfy the discrete maximum …

Mathematical models for flow through porous media typically enjoy the so-called maximum
principles, which place bounds on the pressure field. It is highly desirable to preserve these …

This paper deals with the formulation and numerical implementation of a fully coupled
continuum model for deformation–diffusion in linearized elastic solids. The mathematical …